Find the function value, if possible. (If an answer is undefined, enter UNDEFINED.) \( \varphi(t)=\left(2 t^{2}+3\right) / t^{2} \) (a) \( \varphi(2) \) (b) \( \varphi(0) \) (c) \( q(-x) \) (b)

Evaluate the expression by following steps: - step0: Evaluate: \(\frac{2\left(-x\right)^{2}+3}{\left(-x\right)^{2}}\) - step1: Multiply the terms: \(\frac{2x^{2}+3}{\left(-x\right)^{2}}\) - step2: Simplify: \(\frac{2x^{2}+3}{x^{2}}\) Substitute \( t=2 \) into the expression \( \frac{2t^{2}+3}{t^{2}} \). Evaluate the expression by following steps: - step0: Evaluate: \(\frac{2t^{2}+3}{t^{2}}\) - step1: Substitute: \(\frac{2\times 2^{2}+3}{2^{2}}\) - step2: Calculate: \(\frac{2^{3}+3}{2^{2}}\) - step3: Add the numbers: \(\frac{11}{2^{2}}\) - step4: Simplify: \(\frac{11}{4}\) Let's evaluate the function \( \varphi(t) = \frac{2t^{2} + 3}{t^{2}} \) for the specified values: ### (a) \( \varphi(2) \) To find \( \varphi(2) \): \[ \varphi(2) = \frac{2(2)^{2} + 3}{(2)^{2}} = \frac{2 \cdot 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \] Thus, \( \varphi(2) = \frac{11}{4} \) or \( 2.75 \). ### (b) \( \varphi(0) \) To find \( \varphi(0) \): \[ \varphi(0) = \frac{2(0)^{2} + 3}{(0)^{2}} = \frac{0 + 3}{0} \] This results in division by zero, which is undefined. Therefore, \( \varphi(0) = \text{UNDEFINED} \). ### (c) \( q(-x) \) To find \( q(-x) \): \[ q(-x) = \varphi(-x) = \frac{2(-x)^{2} + 3}{(-x)^{2}} = \frac{2x^{2} + 3}{x^{2}} \] This simplifies to \( q(-x) = \frac{2x^{2} + 3}{x^{2}} \). ### Summary of Results: - \( \varphi(2) = \frac{11}{4} \) - \( \varphi(0) = \text{UNDEFINED} \) - \( q(-x) = \frac{2x^{2} + 3}{x^{2}} \)